From AMS Glossary
A type of low-frequency gravity wave trapped to a vertical boundary, or the equator, which propagates anticlockwise (in the Northern Hemisphere) around a basin.
The flow is parallel to the boundary and in geostrophic balance with the pressure gradient perpendicular to the boundary. The velocity normal to the boundary is identically zero. For a homogeneous ocean, the wave is called a barotropic or external Kelvin wave, and for a stratified ocean, the wave is called a baroclinic or internal Kelvin wave. Near a boundary in a rotating system, a Kelvin wave propagates with wave crests perpendicular to the side wall and wave height greatest at the side wall to the right of an observer looking in the direction of wave propagation. The wave height decreases exponentially from the side wall with an e-folding length scale equal to the Rossby radius of deformation c/f, in which f is the Coriolis parameter and c is the phase speed of the wave in the along-boundary direction. In the shallow water approximation the waves are nondispersive with frequency
in which k is the along-boundary wavenumber and the phase speed
with g the acceleration of gravity and H the mean fluid depth. Related to Kelvin waves in a channel are Poincare waves.